You can fulfill (1) not too hard.

First, the compiler is allowed to compile your program as-if all values of all variables are such that undefined behaviour doesn't happen, but isn't allowed to extract value bounds based on that for the purposes of optimising across more than one expression. So the compiler is allowed to assume pointers aren't NULL where they are dereferenced, because that is undefined behaviour and the compiler either has to assume the pointer isn't NULL, or require proof from the programmer, or refuse to compile any C program with pointer dereferencing because it is potentially invalid C. However, it is not allowed to assume that because a pointer was dereferenced, that it is not NULL. This restriction should be tight enough that

    int a, b;
    ... set a and b ...
    if (a > 0 && b > 0 && (a+b)&(int)(-1) > a) {
        ...
    } else {
        ...
    }

is compiled to something like

    mov eax a
    add eax b
    cmp eax a
    jle .else

Second, you can define "trivially compiled C" for every platform as a set of substitution rules that transform every C operation into machine instructions without any optimization. Such a trivial compilation would have every variable write correspond to a memory write, keep no variables in registers, always compile the same expression to the exact same machine code (except for memory addresses of variables involved), never inline functions etc. But it would still be allowed to e.g. put 32-bit integers in 64-bit registers on the basis that int operations are assumed not to overflow. The committee should define that for every supported platform as a reference C compiler, then require that C compilation produce machine code with observable side-effects for single-threaded execution equivalent to the reference trivially compiled C.